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Obstructions to compatible splittings

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 1501.01389
Source
arXiv
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Abstract

Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which commutes with the map of short exact sequences? The answer is sometimes yes and sometimes no. We define and prove basic properties of an obstruction group to the existence of compatible splittings.

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